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What is the midline equation of {:[y=2sin((pi)/(2)x+3)?],[y=]:}

What is the midline equation of\newliney=2sin⁡(π2x+3)?y=□ \begin{array}{l} y=2 \sin \left(\frac{\pi}{2} x+3\right) ? \\ y=\square \end{array}

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Full solution

Q. What is the midline equation of\newliney=2sin⁡(π2x+3)?y=□ \begin{array}{l} y=2 \sin \left(\frac{\pi}{2} x+3\right) ? \\ y=\square \end{array}
  1. Define Midline: The midline of a sinusoidal function such as y=Asin⁡(Bx+C)+Dy = A\sin(Bx + C) + D is the horizontal line that the function oscillates around. It is given by the equation y=Dy = D, where DD is the vertical shift of the function.
  2. Identify Vertical Shift: In the given function y=2sin⁡((π2)x+3)y = 2\sin(\left(\frac{\pi}{2}\right)x + 3), there is no vertical shift written explicitly. This means that the vertical shift DD is 00.
  3. Calculate Midline Equation: Therefore, the midline equation of the function y=2sin⁡(π2x+3)y = 2\sin(\frac{\pi}{2}x + 3) is y=0y = 0, since that is the horizontal line around which the function oscillates.

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